Berry-Esseen bounds in the entropic central limit theorem

TL;DR

This paper derives bounds similar to Berry-Esseen for how quickly sums of non-i.i.d. variables approach a normal distribution, measured by total variation and relative entropy.

Contribution

It provides new Berry-Esseen bounds in the entropic central limit theorem for non-i.i.d. sums, extending classical results to entropy-based metrics.

Findings

Bounds for total variation distance to normal distribution.

Bounds for relative entropy distance to normal distribution.

Applicable to sums of non-i.i.d. random variables.

Abstract

Berry-Esseen-type bounds for total variation and relative entropy distances to the normal law are established for the sums of non-i.i.d. random variables.